07 MRI
T2* from T2 and field inhomogeneity
1/T2* = 1/T2 + γ ΔB. Extra dephasing from local field offsets.
Listen
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Simulation
T2* from T2 and field inhomogeneity — Change the numbers; the scene follows.
Where it works
MRI scanner
Main magnet
In the main magnet — B₀ sets Larmor frequency and the local field that drives T2*.
Open this machineFormula
Variables
Results
T₂*
T2 star
6.8372ms
R₂′
Inhomogeneous decay rate
133.76s⁻¹
Explanation
What it means
T2* is shorter than T2 because of extra dephasing from field offsets: 1/T2* = 1/T2 + γ ΔB. GRE, SWI and BOLD contrast live on T2*. A 0.5 µT offset already pulls T2* down hard. This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — Main magnet. In the main magnet — B₀ sets Larmor frequency and the local field that drives T2*. MRI physics lives in the magnet, the gradient, and the voxel: Larmor, Ernst, diffusion, and SAR. These relations decide whether a sequence is possible, safe, and worth the time.
MRI scanner · Open this machineHow to use it
Enter tissue T2 (ms) and a local ΔB (µT). Near air/tissue (sinuses) ΔB is large and GRE signal vanishes — that is the susceptibility artefact. Change one input and watch the curve and the simulation follow.
Symbols
- T₂Transverse relaxation80 ms
- ΔBField offset0.5 µT
Worked example
A typical case from the default values: T₂ = 80 ms (Transverse relaxation); ΔB = 0.5 µT (Field offset). Substituting into the relation gives T₂* = 6.8372 ms; R₂′ = 133.76 s⁻¹. These are teaching numbers — align them with your machine.
Typical values give
- T₂* = 6.8372ms
- R₂′ = 133.76s⁻¹
Where it comes from
The displayed formula is the working relation. 1/T2* = 1/T2 + γ ΔB. Extra dephasing from local field offsets. Usual reference: McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: McRobbie
Assumptions & limits
Static Lorentzian/Gaussian offset, not diffusion through gradients (that is T2′ vs ADC). SE refocuses this term; GRE does not.
Pitfalls
γ for ¹H is not γ for ¹³C. Ernst angle needs the true T1 at that field, not a 1.5 T table used at 3 T. SAR scales with B₀² and flip² — a 3 T copy of a 1.5 T protocol is not automatically legal. Static Lorentzian/Gaussian offset, not diffusion through gradients (that is T2′ vs ADC). SE refocuses this term; GRE does not.
Keep this
γ here is in rad s⁻¹ T⁻¹. ΔB in µT. T2 and T2* in ms.
In this specialty